I totally agree with you. You need to ring the room and make sure he is in it before arriving.
You never know if he is just randomly meeting in a lobby and is then taking you who knows where. It will only take 5 mins to put your mind at rest. If it is a "proper" booking, the gentleman should have no problem with that.
Just adding my voice to the chorus - for all the reasons mentioned above, I NEVER meet a new client in a public place. You've got to do timewaster checks on him (and hanging about in a hotel lobby/restaurant/etc looking for someone you've never met before makes that exceptionally challenging, trust me!) and also yes, get the payment up front and checked before you're in public together. And give your security buddy a call, too, cos that's best done after taking payment.
If your new client doesn't mind handing you a wad of cash over the dinner table, which you then count before standing up to ring a friend and say, "Oh yes, he seems fine. Paid alright, no problems. It's gonna be a great booking! Call you when I'm done!" all right in the middle of a fancy restaurant, then fine. But if he's a genuine sort of chap with at least one braincell, he will quickly understand why meeting in private is preferable.
I know sometimes guys have a bit of a fantasy and they want things to be more like a real date. But in that case, I would say that he's free to pay me a 50% deposit by Amazon voucher (I have the most ridiculous list of books and even a fancy camera that I want from there!) and once that's been received, I am perfectly prepared to risk being stood up for the date itself.
As Amy said, though, there's always a chance that someone is trying to set you up and get you out in public so they can watch you and perhaps photograph/film you for God-only-knows what horrid little reasons. Also, if he's a new client, even if he's genuine, you have no idea how he might behave in public - he could show up drunk and start discussing your website details really loudly, or he could bring a friend, or any dreadful scenario you can think of. Best to always meet someone new in quiet surroundings (after doing all your security checks and telling your safety buddy etc, of course!) so that you can suss them out and get the business bit sorted without distractions.